arXiv subjects
Publications and source records attributed to Hee Chul Pak.
An evidence of temporal dis-continuity of the solution in $F^s_{1, \infty}(\mathbb{R}^d)$ is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.
Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end-point Triebel-Lizorkin spaces $F^s_{1, \infty}(\mathbb{R}^d)$ with $s \geq d + 1$ is clarified.
Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique solution is a quadratic function by the Goldbach's conjecture.
Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.
In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale convergence. A compactness theorem is proved to justify this notion.